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SOH-CAH-TOA EAST OF SOH-CAH-TOA EAST OF JAVAJAVA

[Exploring Trigonometric Functions]

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SOH-CAH-TOA SOH-CAH-TOA means many thingsmeans many things

“Hello” “Goodbye” “I love you” “Your slip is showing”“It’s Your turn to take out the trash!!!”

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SOHCAHTOA Also Means: SOHCAHTOA Also Means: “Let’s do Trig!!“Let’s do Trig!!

[SOH] Sine – Opposite – Hypotenuse

[CAH] Cosine – Adjacent – Hypotenuse

[TOA] Tangent – Opposite - Adjacent

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First: A quick Geometry First: A quick Geometry ReviewReview

PARTS

OF A

RIGHT

TRIANGLE

OPPOSITE

ADJACENT

HYPOTENUSE

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So, Sohcahtoa!So, Sohcahtoa!

[…trans. “Let’s do Trig.!”][…trans. “Let’s do Trig.!”]

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We’ll break it into syllables.We’ll break it into syllables.

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SOHSOH-CAH-TOA-CAH-TOA

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SOH: SINE-SOH: SINE-OPPOPP-HYP-HYP

sin = opposite side

hypotenuse

OPPOSITE

ADJACENT

HYPOTENUSE

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SOH-SOH-CAHCAH-TOA-TOA

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CAH: COSINE-CAH: COSINE-ADJADJ-HYP-HYP

cos = adjacent side

hypotenuse

OPPOSITE

ADJACENT

HYPOTENUSE

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SOH-CAH-SOH-CAH-TOATOA

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TOA: TAN-TOA: TAN-OPPOPP--ADJADJ

tan = opposite side

adjacent

OPPOSITE

ADJACENT

HYPOTENUSE

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A QUICK REVIEWA QUICK REVIEW

SOH - sin = Opposite side

Hypotenuse

CAH - cos = Adjacent side

Hypotenuse

TOA - tan = Opposite side

Adjacent side

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APPLICATIONS:APPLICATIONS:

Let’s solve a problem.

Sohcahtoa!

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Check for Understanding.Check for Understanding.

Find

sin =

cos =

tan =

3

4

5

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Check : Don’t Forget!Check : Don’t Forget!

Find

sin = OPP

HYP

cos = ADJ

HYP

tan = OPP

ADJ

3

ADJ

4 OPP

5 HYP

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Check : ANSWERSCheck : ANSWERS

Find

sin = OPP = 4

HYP 5

cos = ADJ = 3

HYP 5

tan = OPP = 4

ADJ 3

3

ADJ

4 OPP

5 HYP

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APPLICATIONS:APPLICATIONS:

Let’s try a different problem.

Sohcahtoa!

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Check for Understanding.Check for Understanding.

Find x

given: cos 60° = 0.5

60°

x

1

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Check for Understanding.Check for Understanding.

Find x

given: cos 60° = 0.5

And don’t forget

SOH-CAH-TOA60°

x

1

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Check : ANSWERCheck : ANSWER

X = 2

How?

60°

x

1

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Check : ANSWERCheck : ANSWER

X = 2

How? Use

SOH – CAH - TOA

cos 60° = .5 = ADJ = 1

HYP x

.5x = 1

x = 2

60°

x

1

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APPLICATIONS:APPLICATIONS:

Let’s try a WORD problem!

Sohcahtoa!

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Find the Height of Mt. Find the Height of Mt. SohcahtoaSohcahtoa

The volcano is rumbling. The Sohcahtoans need to sacrifice a virgin. They know the base of the mountain is 6 miles high. The angle formed from the base to the top is 60°.

How tall is the mountain?

[Use your calculator!!!]

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Find the Height of Mt. Find the Height of Mt. SohcahtoaSohcahtoa

What do we know?

= 60°

Base = 6 miles = 3 miles

2

6 miles

Height

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What else do know?What else do know?

SOH - sin = Opposite side

Hypotenuse

CAH - cos = Adjacent side

Hypotenuse

TOA - tan = Opposite side

Adjacent side

Which one should we use?

6 miles

Height

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Which one?Which one?

SOH - sin = Opposite side

Hypotenuse

CAH - cos = Adjacent side

Hypotenuse

TOA - tan = Opposite side

Adjacent side

6 miles

Height

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WHY??WHY??

tan = Opposite side

Adjacent side

tan 60° (3mi) = h . (3mi)

3 mi

(tan 60°)(3 miles) = h

(0.866)(3) = h

h = 2.598 miles 3 miles

Height

h

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WHY??WHY??

tan = Opposite side

Adjacent side

tan 60° (3mi) = h . (3mi)

3 mi

(0.866 )(3 miles) = h

answer h = 2.598 miles

3 miles

Height

h= 2.598

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WHY??WHY??

tan = Opposite side

Adjacent side

tan 60° = h .

3 miles

(tan 60°)(3 miles) = h

(0.866)(3) = h

h = 2.598 miles 3 miles

Height

h

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WHY??WHY??

tan = Opposite side

Adjacent side

tan 60° = h .

3 miles

(tan 60°)(3 miles) = h

(0.866)(3) = h

h = 2.598 miles 3 miles

Height

h

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EXCELLENT!!!EXCELLENT!!!

You deserve a HAND!

Now, Let’s Work!!!

SOHCAHTOA!!!

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ASSIGNMENTASSIGNMENT

Class Asignment:

pp. 356-359 Problems #’s 1 – 40

Homework:

p. 360 – 361 #’s 3 – 51 multiples of 3

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ResourcesResources

Picture of Sohcahtoa:

[Devil’s Tower] http://www.animationfactory.com/free/nature/nature_page_aa.html